       Re: Problem with Series

• To: mathgroup at smc.vnet.net
• Subject: [mg113940] Re: Problem with Series
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 18 Nov 2010 07:08:18 -0500 (EST)

```You are apparently looking for fLinearizedLinearized

f = Log[Coth[1/2 ArcCosh[Sqrt[1 + x^2]/x]]];

fLinearized =
FullSimplify[Normal[Series[f, {x, 0, 1}]]]

Log[-((2 + x)/(-2 + x))]

fLinearizedLinearized =
Normal[Series[fLinearized, {x, 0, 1}]]

x

Plot[Evaluate[Tooltip /@
{f, fLinearized, fLinearizedLinearized}],
{x, -1, 1}]

Bob Hanlon

---- Themis Matsoukas <tmatsoukas at me.com> wrote:

=============
I was using Series to linearize a function at x=0 but I run into a problem with the specific function below:

f = Log[Coth[1/2 ArcCosh[Sqrt[1 + x^2]/x]]];
fLinearized = Simplify[Normal[Series[f, {x, 0, 1}]]]
Plot[{f, fLinearized, x}, {x, -10, 10}]

Mathematica produces output without complaining but the result does not contain an explicit linear term. Specifically, fLinearized is not a linear function of x, though it does seem to have the same derivative at x=0 as the original function f. The correct answer should be f=x +O[x^2].

Themis

```

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